Integral of sqrt(1 + e^(2x))

u = 1 + e^(2x) ??

Please point me in the right direction. Thank you.

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- Feb 8th 2011, 11:43 AMjsel21Integral of sqrt(1 + e^(2x))
Integral of sqrt(1 + e^(2x))

u = 1 + e^(2x) ??

Please point me in the right direction. Thank you. - Feb 8th 2011, 11:46 AMdwsmith
- Feb 8th 2011, 01:58 PMmr fantastic
integrate Sqrt[1 + Exp[2x]] - Wolfram|Alpha+

Click on Show steps. - Feb 8th 2011, 05:06 PMTheCoffeeMachine

Where

Let , so that , then:

Thus - Feb 8th 2011, 06:10 PMProve It
- Feb 8th 2011, 06:12 PMdwsmith
- Feb 8th 2011, 06:48 PMjsel21
Thanks guys, these posts were very helpful.

- Feb 8th 2011, 06:54 PMKrizalid
there's no much here, just clearing out the clutter and it's easy.

- Feb 8th 2011, 09:12 PMAbu-Khalil
Also

- Feb 9th 2011, 01:03 AMice_syncer
take u^2 = 1 + e^(2x)

so 2udu = 2e^(2x)

which is 2(u^2-1)dx

2udu = 2(u^2-1)dx

dx = u/(u^2-1) du

put it in the question.. it will be u^2/(u^2-1) du = (u^2 - 1 + 1)/(u^2-1)du - Feb 9th 2011, 08:19 AMKrizalid
you did the same as me.

- Feb 9th 2011, 09:57 AMice_syncer
hmm.. sorry

- Feb 9th 2011, 12:57 PMtopsquark
- Feb 9th 2011, 02:43 PMKrizalid
In this case, on Prove's substitution, that forces to and we have that

Of course we coulda taken but that makes non positive.

It all depends on how you fix the angle, but that's more a matter of dealing with definite integrals.